I finally got tired enough of iterating through one of these problems today that I fired up Octave and made this handy Resistor - Voltage chart for 1/4W resistors.
(Click to Enlarge)
Making the chart was fairly simple:
r = logspace(0, 7, 10000); emax = sqrt((0.25).*r); loglog(r,emax) grid title("Maximum Voltage Chart (1/4W)") xlabel("Resistor Value") ylabel("Maximum Voltage") print("ResistorVoltageChart.png")
This is why I love Octave.